To be able find the area of a figure can be it is useful also after leaving school. For example, this knowledge is useful if you do repair, and want to know how many it will be required paints for a surface of any form. Or suddenly you wanted to create a flower bed and to calculate amount of the necessary materials, it is necessary to determine its area.
Instruction
1. It is convenient to work if your figure - a polygon. You will be able always to break it into final number of triangles, and it is enough to you to remember only one formula - calculation of the area of a triangle. So, the area of a triangle is a half from the work of length of its party at length of height which is carried out to this party. Having summarized the areas of separate triangles to which your will transformed more irregular shape, you know the required result.
2. It is more difficult to solve a problem with determination of the area of any figure. Such figure can have not only direct, but also curvilinear borders. There are ways for approximate calculation. Simple.
3. First, you can use a palette. It is the tool from transparent material with the grid of squares or triangles applied on its surface with the known area. Having imposed a palette over a figure for which you look for the area, you recalculate number of your units of measure which block the image. Combine short the closed units of measure with each other, supplementing them in mind to full. Further, having increased the area of one figure of a palette by number which was counted, you learn the approximate area of your any figure. It is clear, that the more frequent grid is put on your palette, the more precisely your result.
4. Secondly, you can in borders of any figure for which you determine the area, to outline the maximum number of triangles. To determine the area of everyone and to put their areas. It will be very approximate result. If you wish, then can determine also separately the area of the segments limited to arches. For this purpose imagine that a segment - a part from a circle. Construct this circle, and later from its center carry out radiuses to edges of an arch. Pieces form among themselves a corner α. The area of all sector is determined by a formula π*R^2*α/360. For each smaller part of your figure you determine the area and receive the general result, having put the received values.
5. The third way is more difficult, but more precisely and for someone, more simply. The area of any figure can be determined by integral calculus. A certain integral of function shows the area from a function graph to an abscissa. The area concluded between two schedules can be determined by subtraction of a certain integral, with smaller value, from integral in the same borders, but with great value. For use of this method it is convenient to transfer your any figure to the system of coordinates and further to define their functions and to work with methods of the higher mathematics into which we will not begin to go deep here and now.